# Electricity is magic!

Electricity is magic!

Getting home after a long day of work, you might turn on the lights, get some food out of the fridge, and put on the TV to watch an episode of your favorite TV show to help you unwind.  Many people never take the time to realize that all of these ordinary scenarios involve electricity.  In fact, almost everything we do and take for granted requires electricity to function—even your car, in its most basic function, requires a battery.  For many people, the mere mention of the word “electricity”, or the words “voltage” and “current”, are enough to send the brain into a combination of panic and indifference.

Electricity is that concept that your teacher tried to explain to your class in high school for maybe a week or two, but somehow

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# Smallest FM Radio Transmitter Created By Columbia University Engineers

Smallest FM radio transmitter just created using graphene by the wizards at Columbia University. This one is pretty cool and I certainly do not want to butcher the idea and explanation behind it all. So let’s read what Holly Evarts has to say.

Written by Holly Evarts

A team of Columbia Engineering researchers, led by Mechanical Engineering ProfessorJames Hone and Electrical Engineering Professor Kenneth Shepard, has taken advantage of graphene’s special properties—its mechanical strength and electrical conduction—and created a nano-mechanical system that can create FM signals, in effect the world’s smallest FM radio transmitter. The study is published online on November 17, in Nature Nanotechnology.

“This work is significant in that it demonstrates an application of graphene that cannot be achieved using conventional materials,” Hone says. “And it’s an important first step in advancing wireless signal processing and designing ultrathin, efficient cell phones. Our devices are much…

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Let’s talk about the least-square solution to linear systems of equations. Let’s say we have the problem

\$latex Ax=b\$

where A is an m-by-n matrix (m rows, n columns), x is an n-element vector, and b is an m-element vector. This is just a standard form of a linear algebra problem. Let’s also assume A is full-rank.

Now’s let’s say \$latex m>n\$, or A is a tall matrix. We call A an overdetermined matrix. Simply put, there are way too many unique linear equations to solve for a unique x vector answer. So what do we do? We can use least-squares formulation of the problem to get some sort of an acceptable answer. If we multiply by sides of the equation by the Hermitian transpose of A, we get

\$latex A^{*}Ax = A^{*}b \\ x = (A^{*}A)^{-1}A^{*}b\$

So we have a least-squares solution for x. For people well-versed in linear…

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